Dolphin 055

*Developed by Dana Lee Ling with the support and funding
of a U.S. Department of Education Title III grant and the support of the College of
Micronesia–FSM. *

In the 1996 summer Olympics in Atlanta the distance versus speed data was presented for the 100m race. The data was as seen in the table.

Distance/m |
Speed/ms^{-1} |

2.5 | 2.3 |

5.0 | 4.4 |

10 | 7.8 |

20 | 10.9 |

30 | 11.8 |

40 | 11.9 |

50 | 12.0 |

60 | 12.0 |

70 | 12.0 |

80 | 12.0 |

90 | 12.0 |

100 | 12.0 |

Use Excel to make an XY graph of this data.

By the appearance of the graph, determine whether the best fit trend line is likely to be exponential, linear, or logarithmic. Put your answer down on your paper.

Insert a trend line for the graph in Excel by double-clicking on the graph and then performing an Insert trend line. Choose the function selected in number two above. Remember to choose "Display equation on chart" on the Option tab to show the equation of the best fit trend line.

Write down the best fit equation displayed.

Open LiveMath. Type in the best fit equation from Excel. Graph the equation using LiveMath.

Add another function to LiveMath and graph it:

Compare y_{1} to the Excel data originally graphed. Which
fits the data better (more closely matches), the Excel function in number 4 or the
logistic function provided in number 6?